UV Laser Source
4.10 Repumping Light
As noted before (→3.2.2) the Doppler cooling transition in Be+
2S1/2(F = 2) ↔ 2P3/2 is not a closed transition. Spontaneous emission to the metastable ground state 2S1/2(F = 1) is possible:
repumping light with a red detuning of ∆ωHFS = 2π·1.250 GHz to the carrier frequency ofλ = 313.1327 nm is required. Taking advan-tage of polarization effects and compensating for residual magnetic fields the repumping light intensity as low as a few percent of the main beam should be sufficient.
We have discussed different options to produce the repumping light.
A set-up of a second laser system would be to expensive. Much more elegant is the generation of the repumping light by a frequency shifter. Studying the commercially available electro-optical and acousto-optical modulators (EOM/AOM), the specific combination of the UV-frequency and the relatively large modulation frequency has shown that a resonant EOM set-up is the most suitable for our requirements.
The propagation of light in anisotropic crystal media was treated with respect to the sum-frequency generation before (→4.1). It was shown that the normal modes of propagation can be determined from the index ellipsoid. In certain types of crystals, the application of an electric field results in a change in both the dimensions and orientation of the index ellipsoid. This is referred to as the electro-Electro-optics
optical effect. A fundamental description of electro-optics (which is in principle similar to the description of propagation in anisotropic media) is found in [84, 68].
4.10.1 Phase Modulation of Light
Electro-optical modulation can be used for a variety of applications.
For our purpose we focus on the specific set-up for phase shifting of light propagating through an electro-optic crystal as shown in Fig. 4.19.
The incident beam is polarized parallel to one of the principal di-electric axes, thus no birefringence occurs. The change in the index of refraction due to application of an electric field Em is described by
∆n= 1
2n3rijEm, (4.82) wheren is the index of refraction without electric field applied and rij is the electro-optical coefficient for the particular orientation of the crystal.
The phase shift after passing the crystal of lengthLEOM is Phase shift
4.10 Repumping Light 101
Input beam Phase modulated
output beam Electro-optic crystal
x y
z
LEOM
V
Figure 4.19: An electro-optical phase modulator (EOM). The optical polarization is parallel to the electrically induced principal dielectric axis, and remains unchanged. The phase of the light wave is shifted according to the applied voltageV.
δ= ωLEOM
c ∆n = ωn3rijEmLEOM
2c . (4.83)
If the bias field is sinusoidal
Ez =Emsinωmt , (4.84) then an incident optical fieldEin =Acosωt will emerge as
Eout =Acos [ωt+δsinωmt] . (4.85) Using the Bessel-function identities we can rewrite (4.85) as
Eout =A£
J0(δ) cosωt+
+J1(δ) cos(ω+ ωm)t−J1(δ) cos(ω+ ωm)t+
+J2(δ) cos(ω+ 2ωm)t+J2(δ) cos(ω+ 2ωm)t+
+J3(δ) cos(ω+ 3ωm)t−J3(δ) cos(ω+ 3ωm)t+. . .¤ . (4.86)
The optical spectrum of the output beam shows sidebands at both Sidebands sides of the optical input frequency in a constant spacing of ωm.
The distribution of energy in the sidebands is a function of the Distribution of energy modulation index δ. Fig. 4.20 shows the relative energy in the
carrier and the first sidebands.
Forδ= 0 we note J0(0) = 1 and J≥1(0) = 0.
4.10.2 Experimental Set-up of the EOM
The experimentally used EOM was custom fabricated by Leysop LTD using an ADP crystal (Fig. 4.21). The electrical bias field
relative intensity
phase modulation indexd
0.2 0.4 0.6 0.8 1
0.2 0.4 0.6 0.8 1
|J1|
|J0|
2 2
Figure 4.20: Energy in the carrier and first sidebands as a function of the modulation indexδ.
SMA 50W
Spacer Crystal
ADP
16 x 2 x 1.9 mm3 Coupling loop
Cavity Top Plate Adjusting
screws - brass
x
45° toy&z
Figure 4.21: Technical drawing of the EOM, side view (top view is a circle). The cavity enhances the electric field for the modulation. The screws on top change the length of the cavity and thus the capacitance of the cavity to allow tuning. The direction of the modulation electric field in the crystal is parallel to the screws. Depending on the specific crystal cut, in our case the change of the refractive index is perpendicular to the electric field, perpendicular to the drawing plane in the direction of propagation of the light, of course. The polarization of the input light has to be horizontal, perpendicular to the electric field.
is enhanced in a microwave cavity surrounding the crystal. The resonance frequency can be adjusted from 1.1 GHz to 1.275 GHz.
It is known that ADP is slightly hygroscopic, which might cause some absorption lines in the UV spectral region arising over the time. This effect has to be kept in mind for the future use; for the time being, the losses of the UV light when passing the EOM are below 10 % and, fortunately, no increase has been observed. Other materials like KD∗P are less critical in terms of UV absorption, but
4.10 Repumping Light 103
a significant modulation depth in this spectral region is available only up to modulation frequencies of 200 MHz.
The modulation frequency ωm = 2π · 1.25 GHz is taken from a Modulation frequency microwave synthesizer (Racal Dana 9087). The signal is amplified
to 28 dBm of microwave power (Minicircuits ZHL-42).
The characteristic data for the use of the EOM are collected in Tab. 4.5.
Characteristics of the EOM device
crystal ADP, (NH4)H2PO4
crystal system tetragonal 42m
modulation frequency ωm = 2π·(1.10. . .1.275) GHz (resonant) transmission >90 % @ 313 nm
power of driver 28 dBm
polarization of input light horizontal (i.e. || optical table)
modulation index δ= 0.54 @ λ= 313 nm, ωm = 2π·1.25 GHz Table 4.5: Characteristics of the EOM device. See text for details.
The modulation indexδwas experimentally measured. To this end, Modulation index two laser beams of which one was passing through the EOM, were
overlapped on the sensitive area of a photodiode and thebeat-signal was subjected to spectral decomposition, as shown in Fig. 4.22.
l/2 EOM
Figure 4.22: Measuring the modulation index δ by a beat-measurement. The two input beams have slightly different frequencies ω1 and ω2,ωbeat :=ω1−ω2. One beam is passing the EOM. The over-lapped beams are detected with a RF photodiode.
Assume the electric fields of the combined light beams to be E1 =Aexp (i(ω1t+δsinωmt)), E2 =Aexp (iω2t) . (4.87)
The detected intensity I =|E1+E2|2 then yields I = 2A2h
1 + cosωbeatt+
+δ 2
³cos (ωbeat−ωm)t−cos (ωbeat+ωm)t´i ,
(4.88)
where higher order sidebands are dropped andωbeat :=ω1−ω2. We note that the sideband terms cancel each other if ωbeat = 0. Thus slightly different input frequencies ω1 and ω2 are required.
The spectrum analyzer shows a symmetric spectrum centered around ωbeat and the modulation depth can be determined from the ratio of the intensities Iωbeat±ωm/Iωbeat =δ/2.
However, the required fast photodiode, input lasers, and other op-tical components were not available for a direct measurement at 313 nm. Equation (4.83) shows that δ ∝ 1/λ. The measurement could hence be performed with two Nd:YAG lasers at 1064 nm. The resonance frequency of the EOM-cavity was adjusted to 1.25 GHz with the two screws on top. Temperature does affect the center fre-quency, so the laboratory is to be kept at a constant temperature to avoid frequent readjustments.
From a measurement of the relative intensities at the beat frequency and in the first side-band the modulation index
δ1064 = 0.16 (4.89)
is determined. Using (4.83) we finally find
δ313 = 0.54. (4.90)
The relative light intensity in the repumping beam is then (Fig. 4.20)
|J1(δ= 0.54)|2
|J0(δ= 0.54)|2 ≈8%, (4.91) sufficient for efficient laser cooling of Be+ (→3.2.2).